Algebra Examples

$4$ , $8$ , $16$ , $32$ , $64$

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by $2$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 2$

Step 2

This is the form of a geometric sequence.

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of $a_{1} = 4$ and $r = 2$ .

$a_{n} = 4 \cdot 2^{n - 1}$

Step 4

Multiply $4 \cdot 2^{n - 1}$ .

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Step 4.1

Rewrite $4$ as $2^{2}$ .

$a_{n} = 2^{2} \cdot 2^{n - 1}$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a_{n} = 2^{2 + n - 1}$

Step 4.3

Subtract $1$ from $2$ .

$a_{n} = 2^{n + 1}$

Step 5

Substitute in the value of $n$ to find the $n$ th term.

$a_{6} = 2^{(6) + 1}$

Step 6

Add $6$ and $1$ .

$a_{6} = 2^{7}$

Step 7

Raise $2$ to the power of $7$ .

$a_{6} = 128$